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Prove statement "tan"^(-1) 1/7+ "tan"^(-...

Prove statement `"tan"^(-1) 1/7+ "tan"^(-1)1/13="tan"^(-1) 2/9`

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L.H.S. `="tan"^(-1) 1/7 +"tan"^(-1) 1/13`
`"tan"^(-1) ((1/7+1/13)/(1-1/7 -1/13))="tan"^(-1)((13+7)/(91-1))`
`"tan"^-1(20/90) ="tan"^(-1) 2/9`=R.H.S.
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MBD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove statement "sin"^(-1) 3/5+ "sin"^(-1) 8/17="cos"^(-1) 36/85

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  2. Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

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  3. Prove statement "tan"^(-1) 1/7+ "tan"^(-1)1/13="tan"^(-1) 2/9

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  4. Prove statement "tan"(-1)1/2 +"tan"^(-1) 1/5 +"tan"^(-1) 1/8 = pi/4

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  5. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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  6. Prove statement "cot"^(-1) 9 + "cosec"^(-1) sqrt41/4 =pi/4

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  7. Prove statement "sin"^(-1)4/5 +2"tan"^(-1) 1/3= pi/2

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  8. Prove statement 4 "tan"^(-1) 1/5 -"tan"^(-1) 1/70 + "tan"^(-1) 1/99 = ...

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  9. Prove statement 2"tan"^(-1) 1/5 + "sec"^(-1) (5sqrt2)/7 +2 "tan"^(-1) ...

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  10. Prove statement "cos"^(-1) 12/13 +2"cos"^(-1) sqrt(64/65) +"cos"^(-1) ...

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  11. Prove statement"tan"^2 "cos"^(-1)1/sqrt3 +"cot"^2 "sin"^-1 1/sqrt5 =6

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  12. Prove statement"cos"" tan"^(-1) " cot sin"^(-1) x =x

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  13. Prove statement "cot"^(-1)("tan"2x) +"cot"^(-1)(-"tan"2x) = pi

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  14. Prove statement "tan"^(-1) x +"cot"^(-1)(x+1)="tan"^(-1)(x^2+x+1)

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  15. Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="...

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  16. Prove statement "cot"^(-1)(pq+1)/(p-q) +"cot"^-1(qr+1)/(q-r) +"cot"^(-...

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  17. Prove statement"tan"^(-1) (a-b)/(1+ab)+"tan"^(-1)(b-c)/(1+bc) +"tan"^-...

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  18. Prove the "tan"^(-1)(2a-b)/(bsqrt3) +"tan"^(-1) (2b-a)/(asqrt3) =pi/3

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  19. Prove the "tan"^(-1) 1/(x+y) + "tan"^(-1) y/(x^2=xy+1) ="tan"^(-1)1/x

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  20. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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